Hi z2_ODI3MjM4amFu,
At the moment, these are both issues that can be tough to overcome when you are looking at the rental market. Landlords are experiencing a high level of demand for their homes, which means they are tending to turn away from any areas that they see as being risks.
Examples include both DSS and pets. For the latter, they see the chance that furnishings and fixtures could be damaged by animals, while some believe they may struggle to keep a steady income if benefits tenants stumble across financial issues.
However, you can still find someone to let you a home. First port of call should be the Zoopla site. Try searching for the area you are looking in, and then on the box on the right, type things like "pets allowed" "DSS accepted" and others into the keyword field.
Your other option is to try talking to the local council, which will be able to pass on a list of landlords to help you through its housing department.
Many thanks,
Scott